Nonlinear oscillatory and monotonic shocks in dense plasmas with ultra-relativistic degenerate electrons

Abstract

In this paper we study the ion acoustic oscillatory and monotonic shocks in dissipative homogeneous magnetized plasmas. The dissipation in the plasma system is considered via kinematic viscosity of ions and quantum effects are included through degeneracy pressure of ultra-relativistic electrons. Korteweg de Vries Burgers (KdVB) equation is derived by using reductive perturbation method. Numerical and analytical solutions of KdVB equation are presented. The transition from oscillatory profile to monotonic shock are studied numerically at different values of kinematic viscosity. We also analyzed the effects of variations of different plasma parameters on the strength of the shock structure in dense plasmas. The relevance of the work to astrophysical plasma conditions such as in compact stars is also pointed out.